I think what most here are saying is that taking the test a 2nd time in May/June will be difficult as kids have finals, AP exams, etc this time of year and its not ideal to also be taking on prepping for the SAT.
I don’t think most kids are excited to have to prep for the SAT/ACT over the summer but if their goal is to score as high as possible taking the exam a second time they make the sacrifice.
Right or wrong, most colleges give a lot of weight in admission to standardized tests (after course rigor and GPA) so taking the time to study properly for it is the difference maker for many students.
Again, you asked the question about when we thought was the best time to take the SAT a 2nd time and I think you got some great advice and reasons why. Good luck, maybe he will kill it the first time and no need for a 2nd test date?